Does anyone else have this problem when trying to open a .BLEND file?
I have the same issue, and I suspect that your notion that you downloaded the zip file rather than the installer is, in fact, the cause of the problem. It appears to me, that you are using a recent version of Windows. In which case, you can try clicking on "start", and in the menu interface, click on "Default Programs" (in my installation, in the right hand column, directly above "Help and Support"). In the resulting menu, click on "Associate a file type or protocol with a program", which will bring up a list of most of the file types present on your system, perhaps after a period of time to load. In the list, right-click on the Blend extension, and in the upper right hand corner, click on the "change program" 

In my installation, when I do this, there is no option to associate the file with Blender, despite the fact that I have about a dozen versions of Blender present on my machine. But each of these is in a separate folder on the desktop of one particular user (I have a half dozen set up, each associated with a particular activity), so that it might be that Windows apparently does not see that the executable programs in those files. It might be that if the unzipped folders containing the various Blender versions were in the root directory of the drive on which they are located, instead of the desktop folder of a particular user, that Windows might be able to see them.

My workaround is to open an instance of Blender, and open new projects from there, and use "open" from the Blender menu to open existing files, and if it's a project I have previously worked on, to use the "open recent" option.